Digital Leadership, Information Entropy, and Stock Price Volatility: Evidence from CEO Social Media Behavior

In the digital economy, social media has become a critical channel through which corporate executives communicate with investors, thereby influencing market expectations and price dynamics. This study examines how CEO social media behavior affects stock price volatility from an information-theoretic perspective combined with deep learning methods. Using Lei Jun (Xiaomi) and Elon Musk (Tesla) as contrasting cases, we analyze executive communication under transactional and transformational leadership styles. Emotional tone, thematic alignment, and diffusion intensity are extracted using BERT and LDA, and incorporated into a Long Short-Term Memory (LSTM) model to forecast short-term stock price movements. To interpret the mechanism behind the predictive results, we introduce a novel metric: Semantic Resonance Dissipation Entropy (SRE). Derived from Kullback-Leibler divergence, this indicator measures the informational friction between executive semantic output and market attention. The empirical analysis shows that incorporating these high-dimensional semantic features significantly improves volatility prediction. Moreover, leadership style is closely associated with distinct entropic regimes: Transactional leadership corresponds to relatively stable semantic patterns and low entropy, whereas transformational leadership is associated with higher entropy and greater semantic dispersion. Following Musk's acquisition of Twitter, the previously unstable information environment evolved into a persistent structural factor priced by the market. These findings suggest that the economic impact of digital leadership depends on limiting information dissipation to ensure signal clarity in financial markets.